Question Number 48118 by ajfour last updated on 19/Nov/18 $$\sqrt{{a}^{\mathrm{2}} {x}^{\mathrm{2}} −{y}^{\mathrm{2}} }+\sqrt{{b}^{\mathrm{2}} {x}^{\mathrm{2}} −{y}^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\left({a}+{b}\right)\sqrt{\mathrm{2}{x}^{\mathrm{2}} +\frac{{x}^{\mathrm{4}} }{{x}^{\mathrm{4}} −{y}^{\mathrm{2}} }} \\ $$$${Find}\:{x}\:{such}\:{that}\:{y}\:{is}\:{minimum}. \\…
Question Number 113444 by Ar Brandon last updated on 13/Sep/20 $$\mathrm{y}''−\mathrm{2ay}'+\left(\mathrm{1}+\mathrm{a}^{\mathrm{2}} \right)\mathrm{y}=\mathrm{te}^{\mathrm{at}} +\mathrm{sint} \\ $$ Answered by Ar Brandon last updated on 13/Sep/20 $$\mathrm{y}''−\mathrm{2ay}'+\left(\mathrm{1}+\mathrm{a}^{\mathrm{2}} \right)\mathrm{y}=\mathrm{te}^{\mathrm{at}}…
Question Number 178847 by zaheen last updated on 22/Oct/22 $${y}={x}\mathrm{sin}\:\left({x}\right) \\ $$$$\frac{{d}^{\mathrm{35}} {y}}{{dx}^{\mathrm{35}} }=? \\ $$ Answered by mr W last updated on 22/Oct/22 $${y}={f}\left({x}\right){g}\left({x}\right)\:{with}…
Question Number 113196 by bobhans last updated on 11/Sep/20 $$\:\mathrm{y}\:=\:\mathrm{sinh}\:^{−\mathrm{1}} \left(\mathrm{sin}\:\mathrm{x}\right)\:,\:\frac{\mathrm{dy}}{\mathrm{dx}}\:=? \\ $$ Answered by MJS_new last updated on 11/Sep/20 $$\left({f}\left({g}\left({x}\right)\right)'={g}'\left({x}\right)×{f}'\left({g}\left({x}\right)\right)\right. \\ $$$$\left(\mathrm{sinh}^{−\mathrm{1}} \:\mathrm{sin}\:{x}\right)'=\mathrm{cos}\:{x}\:×\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\mathrm{sin}^{\mathrm{2}} \:{x}}}…
Question Number 178682 by MikeH last updated on 20/Oct/22 $$\mathrm{Corona}\:\mathrm{virus}\:\left(\mathrm{covid}\:−\mathrm{19}\right)\:\mathrm{is}\:\mathrm{spreading}\:\mathrm{through}\:\mathrm{a} \\ $$$$\mathrm{certain}\:\mathrm{country}.\:\mathrm{Let}\:\mathrm{the}\:\mathrm{constant}\:{S}\:\mathrm{be}\:\mathrm{the}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{people}\:\mathrm{susceptible}\:\mathrm{to}\:\mathrm{infection}.\:\:\mathrm{The}\:\mathrm{infection}\:\mathrm{rate} \\ $$$$\mathrm{is}\:\mathrm{proportional}\:\mathrm{to}\:\mathrm{the}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{the}\:\mathrm{already} \\ $$$$\mathrm{infected}\:\mathrm{people}\:\left({x}\right)\:\mathrm{and}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{susceptible}\:\mathrm{but}\: \\ $$$$\mathrm{but}\:\mathrm{uninfected}\:\mathrm{people}\:\left({S}−{x}\right).\:\mathrm{establish}\:\mathrm{the}\: \\ $$$$\mathrm{differential}\:\mathrm{equation}. \\ $$ Terms…
Question Number 47559 by ajfour last updated on 11/Nov/18 Commented by ajfour last updated on 11/Nov/18 $${Q}.\mathrm{47519}\:\:\left({Solution}\:{attempted}\right) \\ $$ Answered by ajfour last updated on…
Question Number 47532 by 143jesus last updated on 11/Nov/18 $$\sqrt{\mathrm{400}^{\mathrm{2}} +\mathrm{100}^{\mathrm{2}=} } \\ $$ Answered by Joel578 last updated on 11/Nov/18 $$=\:\sqrt{\mathrm{160000}\:+\:\mathrm{10000}}\:=\:\sqrt{\mathrm{170000}}\:=\:\mathrm{100}\sqrt{\mathrm{17}}\:\approx\:\mathrm{412}.\mathrm{31} \\ $$ Answered…
Question Number 47519 by ajfour last updated on 11/Nov/18 Commented by ajfour last updated on 11/Nov/18 $${Find}\:{minimum}\:{area}\:{of}\:\bigtriangleup{ABC} \\ $$$${in}\:{terms}\:{of}\:{ellipse}\:{parameters} \\ $$$${a}\:{and}\:{b}. \\ $$ Answered by…
Question Number 47432 by Necxx last updated on 09/Nov/18 $$ \\ $$$${what}\:{is}\:{the}\:{nth}\:{derivative}\:{of} \\ $$$${e}^{{ax}} \mathrm{sin}\:\left({bx}+{c}\right)? \\ $$ Commented by maxmathsup by imad last updated on…
Question Number 47425 by ajfour last updated on 09/Nov/18 Commented by ajfour last updated on 09/Nov/18 $${Find}\:{b}\:{if}\:{a}=\mathrm{1}\:{and}\:\bigtriangleup{ABC}\:{has} \\ $$$${minimum}\:{area}. \\ $$ Answered by mr W…